https://file.aiquickdraw.com/mathbot/file/1729248588256zcapogz9.jpg

The image shows a problem involving the graph of a system of two linear inequalities. The system includes the following inequalities:

\[
6x + 4y \leq 6
\]
\[
x \geq -1.8
\]
\[
z \geq 5
\]

There is a graph below the problem, displaying the shaded regions corresponding to these inequalities.

The question asks whether to select the **union** or **intersection** of the individual solution sets, based on how the regions overlap in the graph.

### Explanation:
When graphing inequalities, the solution to a system is found by identifying where the regions defined by the inequalities overlap. The solution for the system of inequalities is the **intersection** of the shaded regions, meaning the area where all the conditions (inequalities) are satisfied at the same time.

So, the correct answer is:

- **The intersection of the individual solution sets.**

Let me know if you'd like more details or have further questions!

### Related Questions:
1. What are the general steps to graph a linear inequality?
2. How do you determine if a line should be solid or dashed when graphing inequalities?
3. What is the significance of the union of solution sets for inequalities?
4. How can systems of inequalities be applied in real-life situations?
5. What changes to the system would cause a different intersection region?

### Tip:
Always remember to test a point within the shaded region to verify if it satisfies all inequalities in the system!

Select and graph the option that describes the overall solution set for the system of two linear inequalities: 6x + 4y ≤ 6, x ≥ -1.8, and z ≥ 5. Should the solution be the union or the intersection of the individual solution sets?

Learn how to graph a system of linear inequalities, including 6x + 4y ≤ 6, x ≥ -1.8, and z ≥ 5, and determine whether to use the union or intersection of solution sets. Understand key algebra concepts and learn step-by-step graphing methods, suitable for students in Grades 8-10.

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